I've been working with GitHub for 3 months ago, and there's a whole world out there about GitHub and source control.
Maybe you actually knows this, but I want to share something that I learned in this page
GitHub is just a hosting to the repositories.
But, there's something else ... Git.
Git is and Interface that brings all that the user need to have control and management of the repositories. In other words:
Git is a source control, a tool management for the record of the source code. Git is the tool and GitHub the service to the projects.
Until now, you've been using GitHub, well, I recommended to you, to use as well Git. Even more in this issue that you have right now.
neither of you have made a mistake. Maybe there something that your brother are ignoring.
There're two command that are so common in Git.
> git fetch //Bring all the changes from the remote server > git pull //Fetch down new data from remote server
And I believe that here are your brother's problem. You have your repo up to date, but for some reason your brother not. And this is because he had to bring the new changes (made it in your repo) in his repo in some specific time. And this achieve with those command (if you use Git command line. You can use other tools, like Visual Studio, Eclipse, TortoiseGit, Git Bash, Git Gui). I know that command line sometimes is complicated, but also, it can help you when no one others can.
That's my tip to you. Actually, back days, I saw here in Stackoverflow a question, where the solution was to make a "mirror repository", How it works? Well, Every time that the person make a commit in repo1 (local repository) automatically sent the changes to repo2 (mirror repository... and yeap, that you will place in your brother's computer. But, I can't find it. I promised that I will keep searching that question and as soon as possible I'll share with you.
Maybe this is not an exactly answer for your problem. Have a good day!